Since the invention of the wave gear device by C. W. Musser (Patent Document 1) up to the present day, inventions for devices of various types have been conceived by its originator, as well as by numerous researchers, including the present inventors. Even limiting the discussion to inventions relating to the tooth profile, numerous different types have been proposed. For example, the present inventors proposed in Patent Document 2 an involute tooth profile for the basic tooth profile of a wave gear device; and in Patent Documents 3 and 4 proposed a tooth profile design method in which a method whereby meshing of a rigid internal gear and a flexible external gear of a wave gear device is approximated by a rack is employed, to derive a cusp tooth profile whereby the two gears contact over a wide area. In Patent Document 5, the present inventors further proposed a tooth profile of high ratcheting torque, making possible continuous meshing in a wave gear device.
Ordinarily, a wave gear device has a ring-shaped rigid internal gear, a flexible external gear disposed coaxially to the inside thereof, and a wave generator fitted inside thereof. The flexible external gear is provided with a flexible cylindrical barrel portion, a diaphragm extending in a radial direction from the rear end of this cylindrical barrel portion, and external teeth formed on the outside peripheral face section of the cylindrical barrel portion at the front end opening side thereof. The flexible external gear that forms in a state in which the diaphragm has closed off the rear end opening of the cylindrical barrel portion is termed a cup-shaped flexible external gear, while the flexible external gear that forms in a state in which the diaphragm has extended outward from the rear end of the cylindrical barrel portion is termed a silk-hat-shaped flexible external gear. The flexible external gear of either shape is deflected to an ellipsoidal shape by the wave generator, whereupon the external teeth formed on the outside peripheral face section of the cylindrical barrel portion thereof mesh with the internal teeth of the rigid internal gear, at either end in the long axis direction of the ellipse.
When the flexible external gear is deformed to an ellipsoidal shape by the wave generator, the rim-neutral circle of the external teeth of the flexible external gear in question deforms to a rim-neutral curve of ellipsoidal shape as well. Where w denotes the amount of bending in a radial direction with respect to the rim-neutral circle prior to deformation at a long axis position of this rim-neutral curve, and w0 denotes a regular (standard) amount of bending, which is the value of the radius of the rim-neutral circle divided by the reduction ratio of the wave gear device, the ratio (w/w0) thereof being the deflection coefficient κ. An amount of bending greater than the regular amount of bending (κ>1) is termed positive deflection, whereas an amount of bending less than the regular amount of bending (κ<1) is termed negative deflection.
Here, the external teeth of the flexible external gear having been bent into an ellipsoidal shape, exhibit an increasing amount of bending in a manner substantially proportional to the distance from the diaphragm, going in the tooth trace direction thereof from the rear end portion at the diaphragm side towards the front end portion at the front opening side. Moreover, in association with rotation of the wave generator, sections of the external teeth of the flexible external gear bend repeatedly in a radial direction. Consequently, for example, when the amount of bending in an axis-perpendicular cross section at the center in the tooth trace direction of the external teeth is set to the regular amount of bending (κ=1), a state of positive deflection bending arises at the side towards the front end therefrom, and a state of negative deflection bending arises at the side towards the rear end therefrom. An external tooth profile in which the external teeth are in a state of positive deflection bending along the entirety thereof in the tooth trace direction is termed a positive deflection tooth profile, and an external tooth profile in which the external teeth are in a state of negative deflection bending along the entirety thereof in the tooth trace direction is termed a negative deflection tooth profile.
“Coning” describes a state in which sections of the flexible external gear are bent by the wave generator in this fashion. To date, sufficient account has not been given to a rational method for setting the tooth profile, while taking coning of the external teeth into account. Currently, strong demand for improved load torque performance of wave gear devices exists in the marketplace. To achieve this, there is a need for a rational tooth profile that takes coning of the external teeth into account, whereby continuous meshing is possible over the entire tooth trace.
One of the requirements for a wave gear device is that countermeasures be provided against ratcheting at high reduction ratios. In the case of a high reduction ratio in which the number of teeth exceeds 200, it is necessary to increase the tooth height in order to prevent ratcheting during torque at high load.